The "Mys"Tori Deepens...

This is the latest sign adorning the stairwell at our local Lotteria. Since I took the last photo, the whole place has been completely refurbished and the sign updated to this!

One wonders if the Deep Dark Management caught me snickering as I took the last photo, resulting in the said alterations.

Notice how the English , ermm, "translation" is a lot shorter now. I will have to get on to a higher authority for the specifics of the actual translation (my good friend Miss Tori again).

Needless to say, life in Korea is still interesting from an etmylogical point of view! No "Mys"Tori there!

Arthur Lowe would be proud of this little bit of Math....

It is called historically "Waring's Problem".

This is a little subject that has fascinated me for a while, maybe perhaps (tautology ahoy!) it took me another while to understand what the question actually was.

Basically, the point in question is about the integers (whole numbers).

We all know what a power is do we not? A "power" of a number is the result of multiplying that number by itself so many times. For instance , the number 3 "to the power of " three is 27. That is , 27 is three 3's multiplied together. 1024 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2, or, to put it in "power" language, 1024 is 2 to the power 10 (ten 2's multiplied together). We say 4 is "2 squared" and 8 is "two cubed".

Waring's problem looks at these "powers" a little more deeply.

Take the number 11, for example.

How many squares can you find to sum to 11?

Let's see.....11 = 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1.

Since 1 = 1 squared ( 1 = 1 x 1 ), it takes 11 squares to sum to 11.

No. it does not! I can do it in only five!

11 = (2 x 2) + (2 x 2) + 1 + 1 + 1.

HOLD ON, I can do better than that. I can do it in three....

11 = (3 x 3) + 1 + 1.

Now those are the basics. Waring proposed that all integers can be summed to AT MOST four squares.

Another example. 23.

NOW it starts to get interesting.

23 = 1 + 1 + 1 +.........(23 squares)

23 = 4 + 4 + 4 + 4 + 4 + 1 + 1 + 1 (8 squares)

23 = 9 + 9 + 1 + 1 + 1 + 1 + 1 (7 squares)

23 = 9 + 9 + 4 + 1 (4 squares)

23 CANNOT be summed by less than 4 squares. (Try it!) It is impossible.

This is the problem for squares (numbers multiplied by themselves twice). Waring was not satisfied. He generalised the problem by saying that all integers large enough (I chose 11 because it requires only three squares) need only FOUR squares to add together. In other words, 4 is the lower limit.

What about cubes? (numbers multiplied by themselves three times, such as 3 x 3 x 3 above)? What is the lower limit for them?

Turns out, it is 9. Try it with 23. It also turns out that 23 is the smallest number to require all 9 cubes. Try that as well!

Waring didn't stop there. He supposed that you need just 19 fourth powers (2 x 2 x 2 x 2, etc) is sufficient for all larger integers.

Research has gone on to prove that you need at most 37 fifth powers, all the way up to a staggering 1,051,899 20th powers.

The list goes on, and smacks of Godel yet again. That is, we can't seem to be able to prove the list, just research it, and yet it seems there is no end. Another 'Indecipherable Prepostion', to quine a phrase.

I have often been asked where do these musings come from , and my usual answer is they are like batch programs run on mainframes at night, or virus checkers run in background mode on pc's. The musings are always there, they just surface from time to time. I admit I had to look up the 20th power limit, but that is the only fact that I did look up. All the rest I have learned from casual reading, tv, etc, and mere thought.

Springer's "Main Waring" Final Thought ~~

" Don't Panic! Don't Panic! "

(Only Brits would suss this allusion)

It's a "Mys"tery

Just like many a sundry Oriental Language, Korean, or Hang-gul, sometimes "mis"ses something in the translation of simple texts.

I mean, I have seen "mis"-translations of simple directions but the above has to be an award winner, found above the stairs to the upper floor of the local fast-food chain here (Jung-ma "Lotteria").

I think it was meant to say "Be careful when carrying your meal upstairs".

Wonderful!

Apologies to my Good Korean Friend "Miss" Tori, or shall we say "Enigma"?

The All-Singing, All-Dancing.......

The Ultimate Quest of Physics, rather like the Answer to the Ultimate Question of Life, the Universe and Everything, or the Search for the Holy Grail, is a bit like a gut feeling.

You know it is there, but you cannot QUITE grasp it (yet).

Some call it the "Theory of Everything" and basically, it will be (or wioll haven be) a set of equations that will tell us how the whole shebang (as in big shebang) works.

Others call it a "Grand Unified Theory".

Whatever it wioll haven be called, it will marry the four forces known in nature. People already know the first two, gravity and electromagnetism, but the other two do not come into contact with the general public.

This is because they are only useful when scientists like to look at the science of the very small. They are called the "strong" and the "weak" "nuclear forces. The names are only historic names, but suffice it to say, there ARE four forces at work (as opposed to the three military ones).

Science had a triumph in 1974 when Abdus Salaam and Steven Weinberg came up with the "electroweak" set of equations, which were a combination of the electromagnetic ones, and the equations for the "weak" nuclear force.

Science is a very solid foundation of investigation, and if a new theory is put forward, it has to make new predictions about what will happen when we apply it. The "electroweak" theory predicted three very heavy particles, the W+, the W-, and the Z0, the so-called "intermediate vector boson". At the time, atom smashers were not powerful enough to even look for these, so the physics community decided to build bigger ones to try.

In 1983, after the completion of one of these, we found the Z0. The theory was venerated, and we knew we were on the path to true understanding.

So we now had three theories, gravity, strong force, and electroweak. In including the strong force, theorists easily predicted that if we are to unite the electroweak with it, the proton would have to decay of its own volition in free space.

We have known for a long time that on average, a neutron decays into a proton, an electron and an antineutrino (in about 16 minutes) for decades, but this new prediction was almost more than we could bear.

When we plugged the numbers in, we found that on average, the free proton was expected to decay in about 100 000 000 000 000 000 000 000 000 000 000 years. (1 followed by 32 zeroes). This is a bit hard to measure. To get around this, we had the bright idea of watching that many protons for a year.

No-one has seen anything yet, owing to us having to screen out every other event that could be misconstrued as a proton decay.

Now, it you think THAT is difficult, try merging gravity into all of this. There have been theories, none really creditable, to unite gravity in the same manner. Two are called "supersymmetry" and "supergravity". They predict new particles, of course, but none have ever been detected because gravity is by far the weakest of all the forces.

Einstein tried in vain until his death in 1955, to unite gravity. The "cosmological constant" mistake that he himself admitted to, pales into insignificance when compared with this.

With Einstein's own equations, he proved that gravity was a geometric effect, not a gauge force. With this in mind, as far as I know, and this alone in this post is my opinion, you cannot "marry" gauge forces with geometry. It is akin to saying "let's unite the equations of the wind with the equations of how plastic is made". In other words, the two are totally incompatible.

THIS, not the cosmological constant, was Einstein's Greatest Mistake.

As for the Unified Field Theory, or the Grand Unified Theory as it is now known, we are still studying huge tanks of carbon tetrachloride for that elusive proton decay, in the hope that it will "clean" the strong force.

Some people claim that a new theory, called "String Theory" is the answer to all these questions. It is a fact that this mathematics has strong indications that it may well be the key, but not even the math guys understand the full implications of the math they themselves have discovered. To sum up, the theory involves math in 10, 11 and 26 dimensions, which is all very well, except for one thing - how does one 'prove' the theory right, when one cannot even get to the fifth dimension?

Obviously, a lot of guts are involved in that kind of travel!

The Face of Defeat

(NB Another subjective post - sorry, I will get to the "persistence" of numbers soon)


This is the face of the Ladies' Ice Hockey Goalminder from the Italian team. Her name is Deborah, or, to put it more succinctly, "Deb".

She is "reeling" from a 16-0 defeat by Canada in the recent Winter Olympics.

She is now famous for a completely bad reason - this was the single most heavy defeat by any Ice Hockey team since the beginning of the Winter Olympiade in 1924.

A shut-out of cataclysmic proportions.

AND what is worse, the team upon whom it was inflicted was the Host Nation! !!! (shrieks - computer guys, you know what I mean!) unlimited.

Come Shine but NOT Rain!

NB - ANOTHER subjective post - I shall have to curtail this annoying habit!



Well, the chap on the left had it "right" tonight!

His name is Marcos Baghdatis and he is from Cyprus. His tennis game has now won him a place in the Final of the Australian Open Tennis Tournament.

However, not before high drama.



In the final set, serving for the match, something even more incredible happened.

Rain interrupted play on a Tennis stadium with a roof.

Allow me to repeat that.

RAIN interrupted play on a Tennis stadium with a roof.

One of the most expensive and luxurious stadia in Tennis History, the Rod Laver Arena, in Melbourne Park, Australia, equipped with a retractable roof, had to halt play because the roof was open and nobody noticed that rain was imminent.

The rain drenched the central portion of the court.

Now, indoor courts are designed to be just that - INDOORS. This one, however, has a roof which can be opened to the summer (daylight) sky.

At the most crucial point in the match, the weather people were obviously watching The Match rather than the clouds, because the heavens opened and rain stopped play - on an INDOOR court!

What must poor little Michaella Krajicek be thinking?


(This post is unrefined - It stil needs vernacular adjustments. Does not say what it needs to say yet.)

Come Rain but NOT Shine!

NB This post is purely subjective



Isn't it ironic, that rain can halt play in a tennis tournament, but extreme heat cannot?

Granted, at the Australian Open this year, they have an Extreme Heat policy, which means play is halted if the temperature gets too high.

However, it obviously didn't work for poor Michaella Krajicek, right, who was forced to retire from heat exhaustion today.

Strikes me as wholly unjust when, if rain falls, play is halted, even though there is no danger to the players' health, yet, in extreme heat, play continues, despite the fact it is not the ability to play that is hampered, but the players' health.

Today , Ms Krajicek had to play until she fell ill, when play should have been stopped because of the heat by the Tournament Referee, Peter MacNamee.

On her doctor's advice, she was forced to choose not to play, the result being a forfeit, ie she lost the match.

No match , as far as I know, has ever been forfeited due to the effects of mere rain.

Such "weatherism" should be outlawed!

On Firmly Inedecipherable Prepositions of Mathematics and Related Systems

For those who like logic paradoxes, this one is a beaut, Bruce. It is called

THE PARADOX OF THE UNEXPECTED HANGING.

It concerns a condemned prisoner and his Judge. The man, already sentenced to death by hanging, is told two things by the Judge.

1) “You will be hanged at noon on one day of next week, Monday through Friday.”
2) “The execution will be a surprise to you: You won’t know the day of the hanging until the executioner knocks on your cell door at 1155 on the day of the hanging.”

In his cell, the prisoner reflects thus:

“I can’t be hanged on Friday, since by Thursday night I will know that I will be hanged Friday, so it won’t be a surprise. “

He smiles.

“So if the hanging is not on Friday, it cannot be on Thursday either, since by Wednesday night I will also know that my execution will be on Thursday. “

His smile broadens.

It broadens further when he realises he can extend this logic right up to Monday, coming to the fabulous conclusion that he cannot possibly be hanged at all, because the Judge apparently has made an erroneous statement.

He is really smiling now.

However, he actually has to go beyond surprise into astonishment when, on Tuesday at 1155, the executioner turns up and he is hanged at noon, expiring with the most comical look of surprise on his face you have ever seen.

So what was wrong with the prisoner’s argument? Did the Judge make an erroneous statement? The sentence was carried out to the letter, all in accordance with the Judge’s two statements, yet the prisoner’s logic seems ironclad.

Much has been written about this paradox, and I have my own take on it.

However, surprisingly enough, I will await the comments of those in the know before divulgence.

The True Nature of the Force

One of the most amazing discoveries in all of science, let alone physics, is the discovery of the speed of light.

Yes, I did say "discovery", even though the speed of light had been known (approximately) for many years prior.

For many years, science thought it knew most of electricity and magnetism, that they were deeply related, etc.

So, we continued our research whilst the other guys were measuring the speed of light with varying degrees of accuracy. They usually got about 300,000 km per second.

Meanwhile, us lab physicists continued to study electricity and magnetism. We even discovered two numbers which seemed to be the same for empty space. That is, through our experiments, we got two constants referring to the properties of empty space, as witnessed by electricity and magnetism respectively. The electric one was called "epsilon-0" and the magnetic one "nu-0". In English, they are the "permittivity" and the "permeability" of free space. Once measured, with known values of the other numbers in the experiments, we could go ahead and calculate what would happen if we didn't know all the other numbers.

Meanwhile, the light-speed measuring people found that now, it was clear that the speed of light was a little LESS than 300,000 km per second, something like 299,000.

Then, in 1865, along came James Clerk Maxwell. He thought it might be a good idea to come up with THE set of equations which completely defined electricity and magnetism, or "electromagnetism", as he called it. He believed that they were just manifestations of the same thing. After the research, his equations seemed to lack something. They were not symmetrical. So, he made a correction (it is called "displacement current" now, but to us cynics, a "fudge" would perhaps be more appropriate - as any South Korean stem-cell research scientist would know).

Anyway, this "correction" made a whole, complete set of 4 symmetric equations, one of which (div B =0) predicted that magnetic monopoles did not exist.

A prediction of one of the other equations proved interesting as well. It predicted that under some circustances electric circuits will radiate self-propogating waves out into empty space in all directions, the speed of which was defined by those two constants mentioned earlier. More specifically, these waves would travel at a speed

s = 1/ SQRT(nu-0*epsilon-0)

Mr maxwell was excited. He plugged the known values of the permeability and permittivity into the above equation. as determned by electric and magnetic experiments, turned the handle, and came up with another constant, s, the speed of these new "waves".

He got this:

s = (approximately) 299,790 km per second.

Wait a minute minute! Isn't that the the latest figure for the speed of light our other chaps are trying to measure?

NOW we know what light is! It is simply an electromagnetic wave, of which many more have since been discovered. Radio, radar, microwaves, X-rays, gamma-rays, uv, infra-red, tv, all are part of what we now know to be the "electromagnetic spectrum", where the differents bits named above, differ only in wavelength. Oh, and there is the visible bit , too, that part which we see with our eyes, otherwise konwn as "light".

And all travel at one speed in empty space, 299,799 km per second, which we now call "c".

The implications that "c" was a derived quantity from other constants, and therefore a universal constant in itself, were not realised until Einstein started to address them in 1905, under Special Relativity, but that is another topic and post!

Marry Charisma's!

2006 is upon us and this blog is seriously out of date. The latest post is dated October 15, and is below the 3-jet post. I still have to figure out why.

Meanwhile, checkout my latest brain-teaser.....

"How many people do you have to invite to a party to be able to say there's more than a 50-50 chance of any two having the same birthday?"

Whilst thoughts abound on that, I will be trying to think of more thunks to think a thunking thing about, that "wioll haven be" a new and pointed post about physics.

10 bonus points for those who can suss where "and how" "wioll haven be" came from.

20 bonus points for identifying where "and how" came from!

How times have changed!